We propose two novel approaches, a modified slow cooling (MSC) method and an improved traveling solvent floating zone (I-TSFZ) method, to crystallize materials with narrow liquidus lines. The MSC method uses a flux-poor starting composition to attain sufficient supersaturation, and involves a rapid cooling from high temperature to a proper crystallization temperature to avoid the formation of unwanted phases. The I-TSFZ method uses a very slow growth velocity to grow crystals under small supersaturation, and a steep temperature gradient to precisely control the growth temperature. The MSC method and the I-TSFZ method have been successfully applied to grow spin ladder compounds La4+4nCu8+2nO14+8n (n = 2,3) and a high-T-c, cuprate Bi2Sr2Ca2Cu3O10+delta, respectively,